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Six-fold Symmetry From Protons To Atoms To The Planets!
By!
Ian Beardsley!
Copyright © 2023 by Ian Beardsley"
of 2 73
Abstract………………………………………………………..3
1.0 The Constant k…………………………………………4
2.0 Hydrocarbons………………………………………….8
3.0 Six-fold in the Electric Field………………………12
4.0 Predicting the Proton Radius…………………….19
5.0 The Result……………………………………………….23
6.0 The Hypothesis…………………………………………25
7.0 Rigorous Formulation of Proton-Seconds……28
8.0 Theory of Compounds……………………………….31
9.0 The Constant k Neutron Star……………………..37
10.0 Orbital Velocity………………………………………46
11.0 Conclusion……………………………………………..66
Appendix 1…………………………………………………….68
Appendix 2……………………………………………………69
of 3 73
The manifestations of matter from proton mass and radius, and their fields are shown as
properties of point, plane, and line that open-up in six-fold symmetry. This is all centered
around the life element carbon. We see the planets open up in six-fold symmetry as well. To do
our work we introduce a constant k in units of inverse velocity by suggesting the use of an
intermediary mass that comes from white dwarf stars. We suggest there is another
intermediary mass and k as well based on neutron stars. We suggest that if we want to go
further to explain why six-fold symmetry we have to go into the mathematics of symmetry
breaking and perturbation theory. "
of 4 73
1.0 The Constant k: Warren Giordano writes in his paper The Fine Structure Constant And
The Gravitational Constant: Keys To The Substance Of The Fabric Of Space, March 21, 2019:
In 1980, the author had compiled a series of notes analyzing Einstein’s geometric to kinematic
equations, along with an observation that multiplying Planck’s constant ‘ ’ by ‘ ’, where ‘
is the Fine Structure Constant, and multiplying by yielded Newton’s gravitational constant
numerically, but neglecting any units.
Let’s do that
(6.62607E-34Js)(1+1/137)(1E23)=6.6744E-11 Js
And it works, G is:
G=6.67408E-11 N(m2/kg2)
Let us reformulate this as by introducing Avogadro’s number because multiplying Planck’s
constant ‘ ’ by ‘ ’ is G if multiplied by and Avogadro’s number is
:
Equation 1.1
We just need the right units. We can get these:
Since grams and atom cancel we can work in grams even though our equations are in kilograms.
Let us not write H, since formally it is grams per mole of hydrogen but write
We have:
Or,…
Equation 1.2
Where
Equation 1.3
Let us say we were to consider Any Element say carbon . Then in general
h
1 + α
α
h
1 + α
N
A
= Avaga dro s Nu mber = 6.02E 23atom s /gram
h
(1 + α)
G
N
A
H = 6.0003
kg
2
s
m
N
A
H = 6.02E 23
atom s
gr a m
1gr a m
atom
= 6.02E 23
= 1
gr a m
atom
h
(1 + α)
G
N
A
= 6.0003kg
2
s
m
h(1 + α)N
A
= 6Gx
x = 1.00kg
2
s
m
𝔼
of 5 73
Equation 1.4
We have
and
Because there are six grams of protons in carbon which has 6 protons and 6 neutrons and a
molar mass of 12. We have
12-6=6 grams of protons in the 12 grams of protons and neutrons. Thus
And it follows that
We see in general since the atomic number Z is the number of protons in an atom that in general
this holds for all elements because
And,
Therefore we always have:
Equation 1.5
is not molar mass, and that is a variable determined by ; it is a mole of atoms multiplied
by the number of protons in . The reason we point this out, though it may already be clear, is
we wish to find the physical theory behind it. That is we need to find the physical explanation for
equation 1.4
It is the integer 6 to 3 ten thousandths. Which classifies it as interesting because since it is in
kilograms, seconds, and meters, it may mean these units of measurement have some kind of a
meaning. We can in fact write it:
h
(1 + α)
G
N
A
𝔼 = 6.0003kg
2
s
m
=
6gr a m s
6protons
N
A
=
6(6E 23pr oton s)
6gr a m s
N
A
= 6E 23
h
(1 + α)
G
N
A
= 6.0003kg
2
s
m
𝔼
N
A
=
Z 6E 23protons
Z gra m s
𝔼 =
Z gra m s
Z proton s
N
A
𝔼 = 6E 23
𝔼
N
A
𝔼
𝔼
h
(1 + α)
G
N
A
𝔼 = 6.0003kg
2
s
m
h
(1 + α)
G
N
A
𝔼 = 6.000kg
2
s
m
of 6 73
We know that
The fine structure constant squared is the ratio of the potential energy of an electron in the first
circular orbit to the energy given by the mass of an electron in the Bohr model times the speed of
light squared. To begin our search for the meaning of equation 1.4 we convert x, the factor of
1.00 to astronomical units, years, and solar masses, as these are connected to the orbit
of earth as it relates to the sun. We have:
=
We can now write
Eq 1.6.
This unit of AU/year is very interesting. It is not , which would be the Earth’s orbital
velocity, but is a velocity given by the earth orbital radius to its orbital period, which is quantum
mechanical in nature. It relates to earth as as a state, as we have with atoms, a number. We
multiply both sides by and we have earth velocity on the left and the units stay the same on
the right. But what we will do is return to the form in kg-m-s and leave it as an equation but put
in the Earth mean orbital velocity which is 29.79km/s (Zombeck, Martin V. 1982). We get:
Eq. 1.7
This brings up an interesting question: while we have masses characteristic of the microcosmos
like protons, and masses characteristic of the macrocosmos, like the minimum mass for a star to
become a neutron star as opposed to a white dwarf after she novas (The Chandrasekhar limit)
which is 1.44 solar masses, we do not have a characteristic mass of the intermediary world where
we exist, a truck weighs several tons and tennis ball maybe around a hundred grams. To find
that mass let us take the geometric mean between the mass of a proton and the mass of 1.44
solar masses. We could take the average, or the harmonic mean, but the geometric mean is the
squaring of the proportions, it is the side of a square with the area equal to the area of the
rectangle with these proportions as its sides. We have:
α
2
=
U
e
m
e
c
2
kg
2
s
m
kg
2
1
s
m
(1.98847E 30)
2
M
2
kg
2
1.4959787E11m
AU
year
3.154E 7s
1.8754341E64
M
2
year
AU
h
(1 + α)
G
N
A
𝔼
AU
year
= 8.2172E 32M
2π AU/year
4π
2
h
(1 + α)
G
N
A
𝔼 v
e
= 422.787kg
M
= 1.98847E 30kg
of 7 73
We multiply this by 1.44 to get 2.8634E30kg. The mass of a proton is .
We have the intermediary mass is:
Eq. 1.8
All we really need to do now is divide 1.7 by 1.8 and we get an even number that is the six of our
six-fold symmetry.
Eq. 1.9
The six of our six-fold symmetry.
We have something very interesting here. We have
This is:
Equation 1.9
Where k is a constant, given
Equation 1.10
We can explicitly write the constant k:
Equation 1.11
It was the Indian physicist Chandrasekhar who found the limit in mass for which a white dwarf
will not have its gravity overcome the degeneracy pressure and collapse. The non-relativistic
equation is:
Equation 1.12
Let us approximate 0.77 with 3/4. Since we have our constant
And
Then
m
p
= 1.67262E 27kg
m
i
= (2.8634E 30)(1.67262E 27) = 69.205kg
1
m
i
h
(1 + α)
G
N
A
𝔼 v
e
= 6.1092 6
1
69.205kg
6kg
2
s
m
v
e
= 6
k v
e
= 6
k =
1
800
s
m
k =
1
m
2
i
h
(1 + α)
G
N
A
𝔼
M 0.77
c
3
3
G
3
N
m
4
p
= 1.41
k =
1
m
2
i
h
1 + α
G
N
A
𝔼
m
i
= Mm
p
of 8 73
Equation 1.13
Since our constant k in terms the Chandrasekhar limit is
Equation 1.14
2.0 Hydrocarbons
The natural constants measure the properties of space and time. We can list some of them here:
(Proton Mass)
(Planck Constant)
(Proton Radius)
(Gravitational Constant)
(light speed)
(Fine Structure Constant)
Gravity is a property of space measured by the universal constant of gravity, G:
Equation 2.1
Matter, or inertia, which measures matter’s ability to resist a force is for each particle (protons
and neutrons) we will suggest given by:
Equation 2.2.
Which describes mass per meter over time, which is:
Equation 2.3:
m
i
=
3
2
c
3
3
G
3
m
2
p
1/2
= h /2π
k =
4
3
m
p
8π
3
G
c
3
h
(1 + α) N
A
𝔼
m
P
: 1.67262 × 10
27
kg
h : 6.62607 × 10
34
J s
r
p
: 0.833 × 10
15
m
G: 6.67408 × 10
11
N
m
2
kg
2
c : 299,792, 459m /s
α : 1/137
q
p
= q
e
= 1.6022E 19coulom bs
k
e
= 8.988E 9
Nm
2
C
2
G = 6.674E 11N
m
2
s
2
= 6.674E 11
m
3
s
2
kg
h
Gc
=
kg s
m
1.82E 16
kg s
m
of 9 73
It must be adjusted by the fine structure constant . It is my guess the factor should be which
is 18,769.:
Equation 2.4.
Because the fine structure constant squared is the ratio of the potential energy of an electron in
the first circular orbit to the energy given by the mass of an electron in the Bohr model times the
speed of light squared, that is it represents the ground state. It is
Equation 2.5.
Here we are suggesting that the proton and neutron are the 3-dimensional cross-sections of a
hypersphere. Thus we consider the surface area of a proton, :
Equation 2.6
We take the square root to get meters:
Equation 2.7
We multiply that with the value we have in equation 4.4:
Equation 2.8
We find that the mass of a proton realizes if we divide this by six seconds:
Equation 2.9
That is hydrogen. We see that the element carbon manifests if we divide instead by 1 second:
Equation 2.10
Carbon (C) is the core element of life chemistry and it combines with hydrogen (H) to make the
skeletons of organic matter, the so-called hydrocarbons:
Equation 2.11
Equation 2.12
If we divide 1E-26kgs by something greater than 6 seconds we get fractional protons. The rest of
the elements in the periodic table occur for dividing by something less that 1-second. It seems
the duration of a second is natural. If it is, since it was formed by a calendar based on
α
1
α
2
(1.82E 16kg s /m)(18,769) = 3.416E 12kg s /m)
α
2
=
U
e
m
e
c
2
S
p
S
p
= 4π r
2
p
= 8.72E 30m
2
S
p
= 2.953E 15m
(2.953E 15m)(3.416E 12
kg s
m
) = 1.009E 26kg s
m
p
m
p
=
1E 26
6secon d s
= 1.67E 27kg
m
c
=
1E 26kg s
1secon d
= 1E 26kg = 6pr oton s = 6m
p
m
p
=
1E 26kg s
6secon d s
m
c
=
1E 26kg s
1secon d
of 10 73
reconciling the periods of the moon and the sun in the earth sky, it should be in the Earth-moon
orbital mechanics. I find it is, that (See appendix 1 and appendix 2):
That is, the earth day (86,400 seconds) times the kinetic energy of the moon to the kinetic
energy of the earth is about 1 second (about 1.2 seconds). The earth day changes very little, by
very small amounts over millions of years. The solar system has evolved towards this since the
explosion of life called the Cambrian, and will slowly decay away from it.
1
2.13
I then developed the concept of proton-seconds where time is associated with atoms through the
number of protons they have.
This way of looking at things is to say matter is that which has inertia. This means it resists
change in position with a force applied to it. The more of it, the more it resists a force. We
understand this from experience, but what is matter that it has inertia? In this analogy we are
suggesting a proton is a three dimensional bubble embedded in a two dimensional plane. As
such there has to be a normal vector holding the higher dimensional sphere in a lower
dimensional space. (See Fig. 1) Thus if we apply a force to to the cross-section of the sphere in
the plane there should be a force countering it proportional to the normal holding it in a lower
dimensional universe. It is actually a 4-dimensional hypersphere whose cross-section is a
sphere. This counter force would be experienced as inertia. Since Planck’s constant h is a
measure of energy over time where space and time are concerned it must play a role. Of course
the radius of a proton plays a role since squared and multiplied by it is the surface area of our
proton embedded in space. The gravitational constant is force produced per kilogram over a
distance, thus it is a measure of how the surrounding space has an effect on the proton giving it
inertia. The speed of light c has to play a role because it is the velocity at which events are
separated through time. The mass of a proton has to play a role because it is a measurement of
inertia itself. And alas the fine structure constant describes the degree to which these factors
have an effect. We see the inertia then in equation 6 is six protons over 1 second, by dimensional
analysis.
K E
moon
K E
earth
(Ear th Da y) 1secon d
m
p
=
3r
p
18α
2
4πh
Gc
4π
See Appendix 2: Sexagesimal And The Cosmic Calendar, page 39
1
Fig. 1
of 11 73
Equation 2.14
We find six seconds gives 1 proton is hydrogen:
Equation 2.15
For time t greater than 6 seconds we have fractional protons. For t<6 we the have other
elements.
Is proton-seconds. Divide by time we have a number of protons because it is a mass divided by
the mass of a proton. But these masses can be considered to cancel and leave pure number. We
make a program that looks for close to whole number solutions so we can create a table of values
for problem solving.
By what value would you like to increment?: 0.25
How many values would you like to calculate for t in equation 1 (no more than 100?): 100
24.1199 protons 0.250000 seconds 0.119904 decpart
12.0600 protons 0.500000 seconds 0.059952 decpart
8.0400 protons 0.750000 seconds 0.039968 decpart
6.0300 protons 1.000000 seconds 0.029976 decpart
4.0200 protons 1.500000 seconds 0.019984 decpart
3.0150 protons 2.000000 seconds 0.014988 decpart
2.1927 protons 2.750000 seconds 0.192718 decpart
2.0100 protons 3.000000 seconds 0.009992 decpart
1.2060 protons 5.000000 seconds 0.205995 decpart
1.1486 protons 5.250000 seconds 0.148567 decpart
1.0964 protons 5.500000 seconds 0.096359 decpart
1.0487 protons 5.750000 seconds 0.048691 decpart
1.0050 protons 6.000000 seconds 0.004996 decpart
0.2487 protons 24.250000 seconds 0.248659 decpart
0.2461 protons 24.500000 seconds 0.246121 decpart
0.2436 protons 24.750000 seconds 0.243635 decpart
A very interesting thing here is looking at the values generated by the program, the smallest
integer value 1 second produces 6 protons (carbon) and the largest integer value 6 seconds
produces one proton (hydrogen). Beyond six seconds you have fractional protons, and the rest of
the elements heavier than carbon are formed by fractional seconds. These are the hydrocarbons
the backbones of biological chemistry. Here is the code for the program:
1
α
2
m
p
h 4π r
2
p
Gc
= 6pr oton secon ds = carbon(C )
1
α
2
m
p
h 4π r
2
p
Gc
= 1pr oton 6secon d s = hydr ogen(H )
1
α
2
m
p
h 4π r
2
p
Gc
of 12 73
#include <stdio.h>
#include <math.h>
int main(int argc, const char * argv[]) {
int n;
float value=0, increment,t=0, p=1.67262E-27, h=6.62607E-34,G=6.67408E-11,
c=299792459,protons[100],r=0.833E-15;
do
{
printf("By what value would you like to increment?: ");
scanf("%f", &increment);
printf("How many values would you like to calculate for t in equation 1 (no more than 100?): ");
scanf("%i", &n);
}
while (n>=101);
{
for (int i=0; i<n;i++)
{
protons[i]=((137*137)/(t*p))*sqrt(h*4*(3.14159)*(r*r)/(G*c));
int intpart=(int)protons[i];
float decpart=protons[i]-intpart;
t=t+increment;
if (decpart<0.25)
{ printf("%.4f protons %f seconds %f decpart \n", protons[i], t-increment, decpart);
}}}}
We see the radius of a proton is given by carbon (1 second):
Equation 2.16
The experimental radius of a proton is:
Equation 2.17
3.0 Six-fold in the Electric Field
I construct the electric field as such (Fig. 2): is one component of . Events in
are through time with components and where c is the speed of light. The
electrons and the protons and in the presence of one another cross into giving
themselves acceleration in the and directions.
We have
We suggest
r
p
=
18
3
α
2
m
p
Gc
4πh
= 8.288587 × 10
16
m = 0.829f m
r
p
= 0.833
±
0.014f m
x
3
(x, y, z)
3
(x, y, z)
ct
1
ct
2
q
e
q
p
ct
1
ct
2
x
x
i
j
k
0 ct
1
0
0 0 ct
2
= (ct
1
ct
2
)
i
of 13 73
Equation 3.1
The position of changes in the space of and has travelled to a place in
time, as well. Since ct=meters there is a g such that . Thus since
and that is . Thus g is frequency squared ( ) and we suggest it is
derived from the separation between the charges and . That there is some velocity v such
that . We call upon our equation for 1 second:
··
x (ct
1
ct
2
)
i
x
3
(x, y, z)
t (0,ct
1
, ct
2
)
··
x = g(ct
1
ct
2
)
i
g m =
m
s
2
g =
1
s
2
=
1
t
2
1
s
2
m
s
s =
m
s
2
f
2
q
e
q
p
f =
(
v
x
)
r
p
m
p
h 4π
Gc
= 1secon d
(
v
x
)
2
(c)
r
p
m
p
h 4π
Gc
=
k
e
m
q
2
x
2
Fig. 2
of 14 73
Letting v= from equation 3.16
And we have
Equation 3.2
We get
Equation 3.3
Is carbon. We see the six-fold symmetry that is the carbon is due to the cube having 6
faces. I think I can be more accurate using space expanding in a sphere as opposed to a cube. We
have that
Equation 3.4
Equation 3.5
Equation 3.6.
Equation 3.7.
v
2
(c)
r
p
m
p
h 4π
Gc
= k
e
q
2
m
α
2
6
1
k
k =
4
3
m
p
8π
3
G
c
3
h
(1 + α) N
A
𝔼 =
1
773.5
s
m
1
k
= 773.5
m
s
m = m
p
c
k
e
(
α
2
6
1
k
)
2
h 4π r
2
p
Gc
= q
2
h 4π r
2
p
Gc
=
(6.626E 34)(4π)(0.833E 15)
2
(6.674E 11)(299,792, 459)
= 5.37E 31
q = (0.033)
1
36(18769
2
)
773.5
2
(5.37E 31) = 9.1435E 19C
q
q
p
=
9.1435E 19C
1.602E 19C
= 5.71pr oton s 6pr oton s
α
2
/6
m
p
=
1E 26kg s
6secon d s
m
c
=
1E 26kg s
1secon d
m
p
=
3r
p
18α
2
4πh
Gc
1
α
2
m
p
h 4π r
2
p
Gc
= 6pr oton secon ds = carbon(C )
of 15 73
Equation 3.8.
Equation 3.9
Equation 3.10
Periodic table as cycles of six (3x6=18)
Hydrocarbons: The Skeltons of Life Chemistry
We said essentially at the outset if we consider it more explicitly that the periodic table is
structured the way it is because its cycle of 18 groups is founded in six-fold symmetry because 18
is 6 X 3=2 X 3 X 3 and 6 is 2 X 3 and 2 and 3 are the smallest prime numbers meaning no
number can be reduced further than factors of these, so these are the basis set at the crux of
Nature.
1
α
2
m
p
h 4π r
2
p
Gc
= 1pr oton 6secon d s = hydr ogen(H )
c
k
e
(
α
2
6
1
k
)
2
h 4π r
2
p
Gc
= q
2
q
q
p
=
9.1435E 19C
1.602E 19C
= 5.71pr oton s 6pr oton s
of 16 73
We said that the
hydrocarbons are the
skeleton of life and we
now further point out
that their components
hydrogen and carbon
are in inverse
relationship with one
another, as seen in the
figure to the left which
interprets the
relationship between
carbon and seconds and
hydrogen and seconds
and how they define the
periodicity of the
Periodic Table of the
Elements by inscribing
proton cross-sections in
regular hexagons that
tessellate with one
another and are made
up of tessellations of
equilateral triangles.
The inverse nature is in
that for carbon six
protons pack in one
hexagon around a center
to make a ring and for
the hydrogen the proton
inscribes in one hexagon
touching all sides its
radius the apothems.
of 17 73
We find it useful to write out the constants in terms of their units we have used to describe
space, time, and matter and their properties in the previous sections…
, ,
We have that
Which is the units of the gravitational constant G is
Which is the units of force in Newtons is
The Bohr radius, or mean orbital radius of an electron in hydrogen for its ground state is
Is units of energy in joules.
We now express the inverse relationship between carbon ( ) and hydrogen ( ) by writing
G = N
m
2
kg
2
= kg
m
s
2
m
2
kg
2
=
m
3
kg s
2
h = J s = kg
m
s
2
m s = kg
m
2
s
c =
m
s
r
p
= m
m
p
= kg
hc
m
2
p
=
m
3
kg s
2
hc
m
2
p
=
(6.626E 34)
1.6726E 27E 27)
2
299,792459
1
= 7.10048E 28N
m
2
kg
2
hc
r
2
p
= kg
m
s
2
(6.626E 34)
(0.833E 15m)
2
299,792459
1
= 286,274N
a
0
=
4πϵ
0
2
m
e
e
2
= 5.29177E 11m
hc
a
0
= 7.1E 5J
t
6
= m
p
t
6
= kg s
t
1
=
t
1
6m
p
=
s
kg
hc
m
2
p
t
6
=
hc
m
2
p
6sec m
p
=
m
3
s
hc
r
2
p
t
1
=
hc
r
2
p
1sec
6m
p
=
m
s
of 18 73
We multiply the former with the inverse of the latter:
And we see that the second maps the first into a factor of 6 which is what they should do.
But what we really want to do is is form a geometric mean:
Because it is energy, we will say the energy of our hydrocarbon in hexagonal tension.The
ionization energy of carbon is 1.804051E-18 Joules and that of hydrogen is 2.18E-18 Joules., the
energies to remove an electron (to move it from ground state to infinity). These are very close to
exactly the squares of our 1.4142E-9 Joules for the energy of our hexagonal tension for the
hydrocarbon. Why would we have the square of the ionization energies? Because the energy is
not just over a line, but two lines that form an area, and area is the square of a line. The
ionization energy of hydrogen is given by the Rydberg equation:
where and and A=2.18E-18J
The Electron affinity of carbon is 153.9kJ/mol
Electronegativity of carbon is 2.55
First ionization of carbon is 11.2603eV
IE=11.2603eV=1.8041E-18J.
We have (2.18E-18+1.8E-18)/2=1.99E-18 and
We can predict the radius of a proton if we can derive an expression for 1 second. We approach
that after the next section…
(
hc
m
2
p
6sec m
p
)
(
r
2
p
hc
6m
p
1sec
)
= 6r
2
p
= 4.163E 30m
2
hc
r
2
p
hc
6r
2
p
hc
r
2
p
= 286,274N
hc
6r
2
p
= 47,712N
(
hc
m
2
p
t
6
)(
hc
r
2
p
t
1
)
= 1.4142E 9kg
m
2
s
2
= 1.4142E 9J = 2E 9J
ΔE = A
(
1
n
2
f
1
n
2
i
)
= 2.18E 18J
n
f
=
n
i
= 1
C + IE C
+
+ e
(1.414E 9)
2
= 1.99E 18
of 19 73
4.0 Predicting The Proton Radius We consider two paths, one with velocity c in one
medium, the other with velocity v in another. In order to go from one point two another over
two paths, the refraction is such that the sine of the angle of incidence equals the sine of the
angle of refraction.
We have the two paths are travelled in a time t:
This is the mysterious Nature of reality, the path of least time is taken. This falls under the
general heading The Principle of Least Action, attributed to firstly the French Natural
Philosopher and mathematician Louis Maupertuis of the early eighteenth century. I say
mysterious, because as it is said in physics, for something to know the path of least action and
take it, it is as if it has explored first all paths between A and B to know which one would be the
path of least action. Everything in physics comes to this principle. It is called a principle, not a
theory, law, or rule. Yet it seems to be the way Nature behaves, and it is mysterious. Richard
Feynman applied it to quantum mechanics, probably because the mysterious Planck’s constant
that governs quantum mechanics is in Joule-seconds, energy over time, and this is the terms in
which action is formulated mathematically.
In our scenario here we regard matter, the proton in particular, as the cross-section of a
hypersphere. Our two mediums are hyperspace and space and the least action principle applies
in the same mathematical form. This is abstract cosmology, that really is the underlying
mathematics is common to all systems, that in effect they are manifestations of one another.
We have
We make the approximation
So that
We are saying t=6 seconds is the proton, and r is the radius of a proton r=0.833E-15m. Thus
The radius of a hydrogen atom is .
sin α
sin β
=
v
c
t = r
p
c + v
c v
t
r
c v v = c
t
r
c v = c
v =
r
t
v =
0.833E 15m
6s
= 1.389E 16m /s
R
h
= 1.2E 10m
of 20 73
And we have our one second as a natural constant with respect to the atom. We see it occurs at
t/2 which is at half the radius of a hydrogen atom, which is because we would think we are
looking at one hydrogen atom packing with two hydrogen atoms. We find if we derive the
equation that represents these computations, we have
Where,…
, ,
Radius of hydrogen atom
Remember our constant k equation 4.16 (Don’t forget to divide by two somewhere):
Since we have the equation of the radius of a proton is given by, by evaluating it at one second
which is carbon:
t =
1.2E 10m
1.389E 16m /s
= 863,930 . 8855s
t
2
= 431,965 . 4428s
t
k
= (773.5m /s)(431,965 . 4428s) = 334,125, 270m
334,125, 270m
c
=
334,125, 270m
299,792, 459m /s
= 1.11452193secon d s
v =
r
t
t = 6s =
1
α
2
m
p
h 4π r
2
p
Gc
1
t
= α
2
m
p
Gc
h 4π r
2
p
v =
r
p
t
= α
2
m
p
Gc
h 4π
R
H
= 1.2E 10m
t =
R
h
v
= R
h
1
α
2
m
p
h 4π
Gc
1
k
=
3
4
1
m
p
c
3
h
8π
3
G
1
1 + α
1
N
A
𝔼
1
k
=
3
4
1
m
p
c
3
h
8π
3
G
1
N
A
𝔼
t
ck
=
3 2
16
h
Gπ
1
α
2
m
p
R
H
N
A
𝔼
t
ck
=
3 2
16
6.626E 34
6.674E 11
18769
(1.6726E 27)
2
1.2E 10
6.02E 23
1
π
= 1.12secon d s
r
p
=
18
3
α
2
m
p
Gc
4πh
= 8.288587 × 10
16
m = 0.829f m
of 21 73
And 1 second in terms of the atom is given by
Then the equation for the radius of a proton is:
Equation 4.1.
And since
Then,…
Equation 4.2
Let’s verify equation 4.1:
Remember that in equation 8.1, which is
That, must remain coupled. is determined by the number of protons in .
Making the approximation 9/8~1 we can write equation 2.3 as (We have picked up the fraction
9/8 by making several approximations)
3 2
16
h
Gπ
1
α
2
m
p
R
H
N
A
𝔼
= 1.12secon d s
r
p
=
9
8
2
1
m
p
hc
4π
3
G
R
H
N
A
𝔼
3 2
16
h
Gπ
1
α
2
m
p
R
H
N
A
𝔼
= 1.12secon d s
1
α
2
m
p
h 4π r
2
p
Gc
6
K Eof Moon
K Eof Ear th
Ear th Da y = (6)1.2secon d s
3 2
16
h
Gπ
1
α
2
m
p
R
H
N
A
𝔼
=
K Eof Moon
K Eof Ear th
Ear th Da y
r
p
=
9
8
2
1
1.67E 27
(6.626E 34)(299,792, 459)
(6.674E 11)4π
3
1.2E 10
6.02E 23
= 0.93f m
r
p
=
9
8
2
1
m
p
hc
4π
3
G
R
H
N
A
𝔼
N
A
𝔼
N
A
𝔼
of 22 73
Equation 4.3
Which gives
We form constants:
Equation 4.4
Equation 4.5
And we have the Equation:
Equation 4.6.
We can say that Avogadro’s number is not an arbitrary number because it is such that there are
twelve grams of carbon and carbon is 6 neutrons plus 6 protons equals 12.
We now want to add to this section the equation of the mass of a proton.
Equation 4.7.
r
p
=
1
m
p
hc
2π
3
G
R
H
N
A
𝔼
r
p
= 8.26935E 16m 0.827f m
r
p
=
1
kg
(
kg
m
2
s
)
(
m
s
)
(
kg
s
2
m
3
)
R
H
N
A
=
1
kg
(
kg
)
m
k =
hc
2π
3
G
= 6.93E 9kg
R
H
N
A
𝔼
= 1.99E 34m
r
p
m
p
= k
R
H
N
A
𝔼
m
p
=
1
r
p
hc
2π
3
G
R
H
N
A
𝔼
of 23 73
5.0 The Result Thus we have from section 1.0 the constant k is a velocity:
Equation 1.14
From section 2.0:
2.13
We have six seconds gives 1 proton or hydrogen and 1 second gives 6 protons or carbon:
Equation 2.14
Equation 2.15
We see the radius of a proton is given by carbon (1 second):
Equation 2.16
The experimental radius of a proton is:
Equation 2.17
In section 3.0 we have the charge of a proton:
Equation 3.9
Equation 3.10
In section 4.0 we derived the radius of a proton by coming up with the unit of a second:
k =
4
3
m
p
8π
3
G
c
3
h
(1 + α) N
A
𝔼
m
p
=
3r
p
18α
2
4πh
Gc
1
α
2
m
p
h 4π r
2
p
Gc
= 6pr oton secon ds = carbon(C )
1
α
2
m
p
h 4π r
2
p
Gc
= 1pr oton 6secon d s = hydr ogen(H )
r
p
=
18
3
α
2
m
p
Gc
4πh
= 8.288587 × 10
16
m = 0.829f m
r
p
= 0.833
±
0.014f m
c
k
e
(
α
2
6
1
k
)
2
h 4π r
2
p
Gc
= q
2
q
q
p
=
9.1435E 19C
1.602E 19C
= 5.71pr oton s 6pr oton s
of 24 73
Equation 4.3
Which gives
We form constants:
Equation 4.4
Equation 4.5
And we have the Equation:
Equation 4.6.
This last, equation 4.6 is the most important because it shows how the mass and radius of a
proton is related to the radius of a hydrogen atom divided by Avogadro’s number without units
and the constant of gravity G, Planck’s constant, h, and the speed of light c, which is to scale the
subatomic particles radius of a proton and its mass with the atoms, or elements, of chemistry,
one step up in size, through the Nature of space and energy G, h, and c. Both quantum
mechanically and gravitationally. Let us turn to this…
r
p
=
1
m
p
hc
2π
3
G
R
H
N
A
𝔼
r
p
= 8.26935E 16m 0.827f m
r
p
=
1
kg
(
kg
m
2
s
)
(
m
s
)
(
kg
s
2
m
3
)
R
H
N
A
=
1
kg
(
kg
)
m
k =
hc
2π
3
G
= 6.93E 9kg
R
H
N
A
𝔼
= 1.99E 34m
r
p
m
p
= k
R
H
N
A
𝔼
of 25 73
6.0 The Hypothesis Let us start with the units with which we are working:
And convert these to proton-masses and proton-radii:
Now we find k in these units:
Thus we have:
Thus we see times is approximately one mole, that is the radius of one hydrogen atom
times k is approximately one mole.
Equation 6.1.
So we have
G =
m
3
kg s
2
h = kg
m
2
s
c = m /s
G = 6.67408E 11
m
3
kg s
2
1.67262E 27kg(0.833E 15m)
3
s = 193,131,756
h = 6.62607E 34kg
m
2
s
s
(0.833E 15)
2
(1.67262E 27kg)
= 5.71E 23
c =
(299,792,459m /s)(1sec)
(0.833E 15m)
= 3.6E 23
R
H
=
1.2E 10m
0.833E 15m
= 144,058
k =
hc
2π
3
G
= 6.93E 9kg
k =
(5.71E 23)(3.6E 23)
2π
3
(193131756)
= 4E18pr oton m a sses
r
p
m
p
= k
R
H
N
A
𝔼
r
p
m
p
=
(4E18)(144058)
(6E 23)
=
5.76E 23
(6E 23)
= 0.96 1
R
H
k
R
H
k = 1m ole
of 26 73
Equation 6.3.
We can say the molar mass of hydrogen is
=
This is really what we are saying when we are speaking of the molar mass of hydrogen, that there
is one atom of hydrogen per proton by mass. What we have discovered is
Equation 6.4.
Which is to say mass is inverse relationship to space, i.e. a length is the inverse of a mass.
This by a factor of
Equation 6.5.
Equation 6.6.
Indeed the radius of a proton to the mass of a proton needs to be exactly 1.00 not 0.96, but the
0.96 is close enough to work with. However, the radius of a hydrogen atom is vague and the
value of 1.2E-10 is a construct that satisfies certain models. We can suggest that 144058 is
actually 150,000, in which case (150,000)(4E18) is exactly 6E23 or Avogadro’s number. If we do
this then it is to say the radius of a hydrogen atom is 1.2495E-10m. This could be some sort of a
functional radius in terms of the mechanics of what is going on here, it does not mean 1.2E-10 is
not a functional radius in terms of other mechanical systems. That which we want to do is look
at equation 6.4 so we can understand if the radius of a proton as the inverse of its mass, is
compatible with our model of inertia in fig. 1 which determines equations equations 4.3 and 4.7.
We see then, that a hydrogen atom is 150,000 times bigger than its proton:
R
H
hc
2π
3
G
= 6E 23m
p
r
p
6E 23
atom sH
gr a m
1,67262E 24
gr a m s
proton m ass
1.00
atom sH
proton m ass
r
p
=
R
H
k
N
A
1
m
p
r
p
m
p
R
H
k
N
A
=
(1.2E 10m)(6.93E 9kg)
(6E 23)
= 1.386E 42
m
kg
R
H
k
N
A
=
(144058r
p
)(4E18m
p
)
(6E 23))
= 0.96
r
p
m
p
= 1
r
p
=
1
m
p
hc
2π
3
G
R
H
N
A
𝔼
m
p
=
1
r
p
hc
2π
3
G
R
H
N
A
𝔼
1.2495E 10m
0.833E 15m
= 150,000
of 27 73
And here is the innovation: We usually think of the building blocks forming first, like the
protons, as building blocks for something of which they are a part, like hydrogen atoms, which
are a proton with an electron orbiting them. But I do not think reverse thinking should be over-
looked, that it may be reasonable to suggest that protons are not necessarily the cause of atoms,
like the hydrogen atom here, but that atoms are the cause of protons, that protons formed to
accommodate atoms, not vice versa. In which case we want to now look at the volume of a
hydrogen atom, and find how many protons and neutrons fit in it if its density is to equal
carbon. We look at carbon because we are concerned with our equations of hydrocarbons, the
skeletons of life that are characteristic of our inertia equations in section 2.0:
Equation 2.14
We find six seconds gives 1 proton is hydrogen:
Equation 2.15
Firstly, our hydrogen volume equation is:
The density of carbon is:
We write
With the mass of a proton equal to the mass of a neutron this is carbon-11 also called carbane
which is unstable and decays with a half-life of 20.4 minutes to Boron-11. Boron 11 is not only
stable, but is boron’s most abundant isotope at 80.1% of the atoms in any natural sample. The
other stable isotope is Boron-10 at 19.8%. Boron is just before carbon in the periodic table of
elements giving it atomic number 5. Thus carbon-12, around which molar mass was defined for
all of the elements is 6 protons and 6 neutrons. My suggestion here that in order for a
hydrocarbon, such as the simplest, methane CH4, must require a hydrogen atom to have a
volume on the order of fitting carbons 6 protons and 6 neutrons. We see here it does, and that it
does especially in light of a hydrogen atoms volume is ambiguous in that its size is described in
terms of the distance of its electron from its proton, which changes as the electron jumps from
1
α
2
m
p
h 4π r
2
p
Gc
= 6pr oton secon ds = carbon(C )
1
α
2
m
p
h 4π r
2
p
Gc
= 1pr oton 6secon d s = hydr ogen(H )
V
H
=
4
3
π R
3
H
=
4
3
π (1.2495E 10)
3
= 8.1714173E 30
kg
m
3
2.26
g
cm
3
= 2,260
kg
m
3
2,260 = n
1.67262E 27kg
8.17E 30m
3
n = 11protons
of 28 73
orbit to orbit. In fact carbon-11 does fit exactly in this definition for a radius for hydrogen. But it
decays into boron-11 which does then fit perfectly, and as we shall see boron plays a pivotal roll
in our theory, but to show that we need to formulate proton-seconds more rigorously, which we
will do now…
7.0 Rigorous Formulation of Proton-Seconds
We can actually formulate this differently than we have. We had
But if t1 is not necessarily 1 second, and t6 is not necessarily six seconds, but rather t1 and t2 are
lower and upper limits in an integral, then we have:
Equation 7.1
This Equation is the generalized equation we can use for solving problems. Essentially we can
rigorously formulate the notion of proton-seconds by considering
Equation 7.2
Is protons-seconds squared where current density is and ( can also be
). We say
Equation 7.3
Keeping in mind q is not charge (coulombs) but a number of charges times seconds, here a
number of protons. It is
Equation 7.4
Dividing Equation 7.2 through by t:
Equation 7.5
1
t
1
1
α
2
m
p
h 4π r
2
p
Gc
= 6pr oton s
1
t
6
1
α
2
m
p
h 4π r
2
p
Gc
= 1pr oton
1
α
2
m
p
h 4π r
2
p
Gc
t
2
t
1
1
t
2
dt =
t
qd t = t
2
S
ρ(x, y, z)d x d y
J = ρ
v
ρ = Q /m
3
ρ
Q /m
2
Q =
V
ρdV
=
1
α
2
m
p
h 4π r
2
p
Gc
1
α
2
m
p
h 4π r
2
p
Gc
t
dt
t
= t
S
ρ(x, y, z)d x d y
of 29 73
Which is proton-seconds. Dividing through by t again:
Equation 7.6
We see that if where and then J is I/m2 (current per square meter)
is analogous to amperes per per square meter which are coulombs per second through a surface.
Thus we are looking at a number of protons per second through a surface. Thus we write:
Is carbon where 0.5 seconds is magnesium (Mg) from the values of time corresponding to
protons in the output from our program and 1.0 seconds is carbon (C). We see we have the
following theorem:
Equation 7.7
So as an example,…
Is fluorine (F). Divide by xy with x=y=1 and we have current density. And multiply by 1 second
which is carbon and we have protons per square meter.
!
1
α
2
m
p
h 4π r
2
p
Gc
t
dt
t
2
= pr oton s
J = ρ
v
ρ = Q /m
3
v = m /s
1
α
2
m
p
h 4π r
2
p
Gc
t
C
t
Mg
dt
t
2
= 6
1.0
0.5
t
2
dt = 6(1 2) = 6
1
α
2
m
p
h 4π r
2
p
Gc
t
dt
t
3
=
S
J d
S
1
α
2
m
p
h 4π r
2
p
Gc
1.0
0.5
dt
t
3
=
S
J d
S = 3
(
1
1
0.25
)
= 9
protons
secon d
J(x, y, z) = (0,0, J ) = J
k
d
S = d x d y
k
J d
S = (0,0, J ) (0,0, d x d y) = Jd x d y
of 30 73
We are now equipt to do computations in proton-seconds. We use equation 3.6 from two to
three, the smallest prime numbers that multiply to make six-fold symmetry in our hexagonal
proton that we found described its radius (My feeling is we introduce the factor of 2 because
carbon is 6 protons +6 neutrons and 2 times 6 is twelve):
Now we integrate from phosphorus is 15 protons=0.396 seconds to aluminum is 13 protons =
0.462 seconds which is to integrate across silicon (divide your answer 10 by 2 to get protons):
By what value would you like to increment?: 0.006
How many values would you like to calculate for t in equation 1 (no more than 100?): 100
251.2490 protons 0.024000 seconds 0.248978 decpart
59.1174 protons 0.102000 seconds 0.117416 decpart
50.2498 protons 0.120000 seconds 0.249805 decpart
40.1998 protons 0.150000 seconds 0.199844 decpart
37.2221 protons 0.162000 seconds 0.222080 decpart
27.1621 protons 0.222000 seconds 0.162058 decpart
25.1249 protons 0.240000 seconds 0.124907 decpart
20.0999 protons 0.300000 seconds 0.099916 decpart
17.0338 protons 0.354000 seconds 0.033823 decpart
16.2096 protons 0.372000 seconds 0.209604 decpart
15.2272 protons 0.396000 seconds 0.227202 decpart
14.1549 protons 0.426000 seconds 0.154862 decpart
13.2236 protons 0.456000 seconds 0.223620 decpart
13.0519 protons 0.462000 seconds 0.051885 decpart
12.1084 protons 0.498000 seconds 0.108375 decpart
11.1666 protons 0.540000 seconds 0.166615 decpart
11.0439 protons 0.546000 seconds 0.043906 decpart
10.1515 protons 0.594000 seconds 0.151471 decpart
Equation 7.8
Silicon can be doped with phosphorus to make negative (n-type) silicon that semi-conducts thus
enabling the construction of logic circuits that you can use to make computing machines. But
this must be joined with positive (p-type) silicon which usually uses boron, but boron is in the
same group as aluminum, just above it. This results in a theory for AI elements as mathematical
constructs, that we will go into now.
2
α
2
m
p
h 4π r
2
p
Gc
t
dt
t
2
= pr oton s
2
α
2
m
p
h 4π r
2
p
Gc
t
Al
t
P
dt
t
3
= 6(6.376 4.685) = 5proton s /secon d = boron
of 31 73
8.0 Theory of Compounds
Above we see the artificial intelligence (AI) elements pulled out of the periodic table of the
elements. As you see we can make a 3 by 3 matrix of them and an AI periodic table. Silicon and
germanium are in group 14 meaning they have 4 valence electrons and want 4 for more to attain
noble gas electron configuration. If we dope Si with B from group 13 it gets three of the four
electrons and thus has a deficiency becoming positive type silicon and thus conducts. If we dope
the Si with P from group 15 it has an extra electron and thus conducts as well. If we join the two
types of silicon we have a semiconductor for making diodes and transistors from which we can
make logic circuits for AI.
As you can see doping agents As and Ga are on either side of Ge, and doping agent P is to the
right of Si but doping agent B is not directly to the left, aluminum Al is. This becomes important.
I call (As-Ga) the differential across Ge, and (P-Al) the differential across Si and call Al a dummy
in the differential because boron B is actually used to make positive type silicon.
That the AI elements make a three by three matrix they can be organized with the letter E with
subscripts that tell what element it is and it properties, I have done this:
Thus E24 is in the second row and has 4 valence electrons making it silicon (Si), E14 is in the
first row and has 4 valence electrons making it carbon (C). I believe that the AI elements can be
organized in a 3 by 3 matrix makes them pivotal to structure in the Universe because we live in
three dimensional space so the mechanics of the realm we experience are described by such a
matrix, for example the cross product. Hence this paper where I show AI and biological life are
mathematical constructs and described in terms of one another.
We see, if we include the two biological elements in the matrix (E14) and and (E15) which are
carbon and nitrogen respectively, there is every reason to proceed with this paper if the idea is to
show not only are the AI elements and biological elements mathematical constructs, they are
described in terms of one another. We see this because the first row is ( B, C, N) and these
happen to be the only elements that are not core AI elements in the matrix, except boron (B)
which is out of place, and aluminum (Al) as we will see if a dummy representative makes for a
mathematical construct, the harmonic mean. Which means we have proved our case because the
first row if we take the cross product between the second and third rows are, its respective unit
vectors for the components meaning they describe them.
E
13
E
14
E
15
E
23
E
24
E
25
E
33
E
34
E
35
of 32 73
The Computation
And silicon (Si) is at the center of our AI periodic table of the elements. We see the biological
elements C and N being the unit vectors are multiplied by the AI elements, meaning they
describe them. But we have to ask; Why does the first row have boron in it which is not a core
biological element, but is a core AI element? The answer is that boron is the one AI element that
is out of place, that is, aluminum is in its place. But we see this has a dynamic function.
The Dynamic Function
The primary elements of artificial intelligence (AI) used to make diodes and transistors, silicon
(Si) and germanium (Ge) doped with boron (B) and phosphorus (P) or gallium (Ga) and arsenic
(As) have an asymmetry due to boron. Silicon and germanium are in group 14 like carbon (C)
and as such have 4 valence electrons. Thus to have positive type silicon and germanium, they
need doping agents from group 13 (three valence electrons) like boron and gallium, and to have
negative type silicon and germanium they need doping agents from group 15 like phosphorus
and arsenic. But where gallium and arsenic are in the same period as germanium, boron is in a
different period than silicon (period 2) while phosphorus is not (period 3). Thus aluminum (Al)
is in boron’s place. This results in an interesting equation.
Equation 8.1
A = (Al, Si, P )
B = (G a, Ge, As)
A ×
B =
B
C
N
Al Si P
Ga Ge As
= (Si As P G e)
B + (P G a Al A s)
C + (Al Ge Si G a)
N
A ×
B = 145
B + 138
C + 1.3924
N
A = 26.98
2
+ 28.09
2
+ 30.97
2
= 50g /m ol
B = 69.72
2
+ 72.64
2
+ 74.92
2
= 126g /m ol
A
B = A Bcosθ
cosθ =
6241
6300
= 0.99
θ = 8
A ×
B = A Bsin θ = (50)(126)sin8
= 877.79
877.79 = 29.6g /m ol Si = 28.09g/m ol
Si(A s G a) + Ge(P Al )
SiG e
=
2B
Ge + Si
of 33 73
The differential across germanium crossed with silicon plus the differential across silicon
crossed with germanium normalized by the product between silicon and germanium is equal to
the boron divided by the average between the germanium and the silicon. The equation has
nearly 100% accuracy (note: using an older value for Ge here, it is now 72.64 but that makes the
equation have a higher accuracy):
Due to an asymmetry in the periodic table of the elements due to boron we have the harmonic
mean between the semiconductor elements (by molar mass):
Equation 8.2
This is Stokes Theorem if we approximate the harmonic mean with the arithmetic mean:
We can make this into two integrals:
Equation 8.3
Equation 8.4
28.09(74.92 69.72) + 72.61(30.97 26.98)
(28.09)(72.61)
=
2(10.81)
(72.61 + 28.09)
0.213658912 = 0.21469712
0.213658912
0.21469712
= 0.995
Si
B
(A s G a) +
Ge
B
(P Al ) =
2SiGe
Si + Ge
0.213658912 = 0.21469712
0.213658912
0.21469712
= 0.995
S
( × u ) d S =
C
u d r
1
0
1
0
[
Si
B
(As Ga) +
Ge
B
(P Al )
]
d x d y
1
Ge Si
Ge
Si
xd x
1
0
1
0
Si
B
(As Ga)d ydz
1
3
1
(Ge Si)
Ge
Si
xd x
1
0
1
0
Ge
B
(P Al )d xdz
2
3
1
(Ge Si)
Ge
Si
yd y
of 34 73
If in the equation (The accurate harmonic mean form):
Equation 8.5
We make the approximation
Equation 8.6
Then the Stokes form of the equation becomes
Equation 8.7
Thus we see for this approximation there are two integrals as well:
Equation 8.8
Equation 8.9
By making the approximation
In
We have
Equation 8.10
Si
B
(As Ga) +
Ge
B
(P Al ) =
Ge Si
Ge
Si
dx
x
2SiGe
Si + Ge
Ge Si
1
0
1
0
[
Si
B
(As Ga) +
Ge
B
(P Al )
]
dyd z =
Ge
Si
d x
1
0
1
0
Si
B
(As Ga)d ydz =
1
3
Ge
Si
dz
1
0
1
0
Ge
B
(P Al )d ydz =
2
3
Ge
Si
dz
2SiGe
Si + Ge
Ge Si
Si(As Ga)
B
+
Ge(P Al )
B
=
2SiGe
Si + Ge
Si
ΔGe
ΔS
+ Ge
ΔSi
ΔS
= B
of 35 73
is the differential across Si, is the differential across Ge
and is the vertical differential.
We say (Phi) is given by
and
And
=1.618
=0.618
(phi) the golden ratio conjugate. We also find
Equation 8.11
We can go straight down group 14 to form the rest of our differentials:
It is amazing how accurately we can fit these differentials with an exponential equation
for the upward increase. The equation is
This is the halfwave:
Since B/Al=10.81/26.98=
0.40
And Ag/Cu =107.87/63.55=
ΔSi = P Al
ΔGe = As Ga
ΔS = Ge Si
Φ
a = b + c
a
b
=
b
c
Φ = a /b
ϕ = b/a
ϕ
(ϕ)ΔGe + (Φ)ΔSi = B
ΔC = N B = 14.01 10.81 = 3.2
ΔSi = P Al = 30.97 26.98 = 3.99
ΔGe = As Ga = 74.92 69.72 = 5.2
ΔSn = Sb In = 121.75 114.82 = 6.93
ΔPb = Bi T l = 208.98 204.38 = 4.6
y(x) = e
0.4x
+ 1.7
y(x) = e
2
5
x
+
17
10
of 36 73
1.697
Where B and Al are the
differential across silicon
and Ag and Au are the finest
conductors of electricity, we
have
Equation 8.12
y(x) = e
(B/Al)x
+
Ag
Cu
of 37 73
9.0 The Constant k Neutron Star
We see our constant k works with the gravitational constant G to predict the radius of a
proton, and with the electric constant to predict the charge of electron as a result of
the six-fold symmetry of the core life element carbon. It follows from our idea of an
intermediary mass!
Where M is given by the Chandrasekhar limit for a white-dwarf star not to collapse:
Giving for k
Which is 1/k=773.5 m/s. There is another kind of star we can use as the limiting factor
for determining a constant k with a different value, a so-called neutron star. The
Chandrasekhar limit is determined by the idea that it resists collapse from electron
degeneracy pressure which is the only thing countering its gravity because it does not do
nuclear fusion. By the Pauli exclusion principle there is pressure from electron
degeneracy because it says that two or more identical particles with half integer spins
cannot occupy the same quantum state within a quantum system simultaneously, which
means the electrons are in motion.
A neutron star is the smallest and densest star we know of because it is made of
neutrons right up against one another giving them near the density of a neutron. They
are the collapsed core of a supergiant from masses of ten to twenty-five solar masses.
They resist collapse by neutron degeneracy pressure in contrast to white dwarves with
electron degeneracy pressure by the same Pauli exclusion principle. While we have an
equation predicting the upper-limit for their mass, it is only a ballpark figure because we
don’t know in quantum mechanics what the properties of neutrons are at such
pressures, however we have been able to experimentally get a value that is thought to be
accurate by observations of actual neutron stars. That value is (About two solar
masses). If its mass exceeds that the neutron star will collapse into a blackhole. Thus we
have another value to obtain an intermediary value for mass, and hence another k. We
will call it . We have
k
e
m
i
= Mm
p
M 0.77
c
3
3
G
3
N
m
4
p
= 1.41
k =
4
3
m
p
8π
3
G
c
3
h
(1 + α) N
A
𝔼
2.16
k
n
m
i
= 1.67262E 27)(1.989E30)(2.16) = 84.770kg
of 38 73
This in contrast to for a white dwarf of 69.205 kg. That is a ratio of 1.2. We have the
value of
Or
In contrast to
The great thing about working with the white dwarf star was that we have an equation
for it, the Chandrasekhar limit so we have a more complete equation for k in that
scenario
That is we are in that scenario not limited to
But the result of k for a neutron star does have some interesting integer properties with the
planets. Where k produced close to the six of our sixfold symmetry using the orbital velocity of
the earth
We have even closer integers with many of the planets for . I have made a program that
computes protons for any incremental integer steps of k staring where you want for k incase you
want to guess there are still more values for k that play a role in any theory you would want to
put forth. I have run it for both k and . It includes the data for all of the orbital velocities of all
the planets and shows the integer values for all of the planets for both k and . I provide the
code incase you want to run the program to play with ideas. It uses our equation of section 3.0
,
The code is (written in c):
m
i
k
n
=
(6.62607E 34)(1.0073)
6.67409E 11
(6.02E 23)
1
84.770
2
= 0.0083779s/m
1
k
n
= 11.936
m
s
12
m
s
1
k
= 773.5
m
s
k =
4
3
m
p
8π
3
G
c
3
h
(1 + α) N
A
𝔼
k =
1
m
2
i
h
(1 + α)
G
N
A
𝔼
k v
e
= 6
k
n
k
n
k
n
c
k
e
(
α
2
6
1
k
)
2
h 4π r
2
p
Gc
= q
2
q
q
p
=
9.1435E 19C
1.602E 19C
= 5.71pr oton s 6pr oton s
of 39 73
#include <stdio.h>
#include <math.h>
int main(int argc, const char * argv[]) {
float x, pi=3.141592654, h=6.62607, G=6.67408, c=299792459,r=0.833;
x=sqrt((h*4*pi*r*r)/(G*c));
//sqrt(1E-11/(1E-34)*(1E-15)(1E-15))=3.162278E27//
printf("x= %fE-31 \n", x*3.162278*10000);
float y,k_e=8.988E9, alpha2=0.000053279;
y=(c/k_e)*(0.166667*alpha2)*(0.166667*alpha2)*1E12;
printf("y= %fE-12 \n", y);
float a=1.188832E-21, charge= 1.602E-19,k, z, q ;
x=5.373682;
y=2.630080;
//z=(x*y)=1.413321E-42//
z=1.413321;
printf("(xy)= %fE-42 \n", z);
//a=sqrt(1.413321-42)=1.188832//
q=a*(772.5)*(1E19);
printf("q= %fE-19 \n", q);
printf("What is your value for 1/k? Our theoretical 1/k is 773.5: \n");
scanf("%f", &k);
float q1=9.183727E-19, protons;
q1=a*k;
protons=(q1/charge);
printf("q/charge= %f protons \n", protons);
of 40 73
//Begin Program//
float qq[100], increment;
int n;
do
{
printf("What value do you want to start at for 1/k?: ");
scanf("%f", &k);
printf("By what value do you want to increment? ");
scanf("%f", &increment);
printf("How many values would you like to calculate for q/proton (no more
than 100?): ");
scanf("%i", &n);
}
while (n>=101);
{
for (int i=0; i<n;i++)
{
k=k+increment;
qq[i]=a*k/charge;
{ printf("%f protons %f k \n", qq[i], k);
}}
{
printf("Here are the orbital velocities for the planets: \n");
printf("Mercury 47,890 m/s \n");
printf("Venus 35,030 m/s \n");
printf("Earth 29,790 m/s \n");
printf("Mars 24,130 m/s \n");
printf("Jupiter 13,060 m/s \n");
printf("Saturn 9,640 m/s \n");
printf("Uranus 6,810 m/s \n");
printf("Neptune 5,430 m/s \n");
}}
{
int i=1;
do
{
float kay,v,integer;
printf("Input a value for k: \n");
scanf("%f", &kay);
printf("Input a planetary orbital velocity: \n");
scanf("%f", &v);
integer=sqrt((1/kay)*v);
printf("integer = %f \n", integer);
printf("Would you like to do another? 0=no, 1=yes \n");
scanf("%i", &i);
}
while (i!=0);
printf("Thank you. \n");
}}
And we can run the program for k and :
k
n
of 41 73
x= 5.373682E-31
y= 2.630080E-12
(xy)= 1.413321E-42
q= 9.183727E-19
What is your value for 1/k? Our theoretical 1/k is 773.5:
100
q/charge= 0.742092 protons
What value do you want to start at for 1/k?: 100
By what value do you want to increment? 10
How many values would you like to calculate for q/proton (no more than 100?):
100
0.816302 protons 110.000000 k
0.890511 protons 120.000000 k
0.964720 protons 130.000000 k
1.038929 protons 140.000000 k <——————One proton (hydrogen) is k=140
1.113139 protons 150.000000 k
1.187348 protons 160.000000 k
1.261557 protons 170.000000 k
1.335766 protons 180.000000 k
1.409976 protons 190.000000 k
1.484185 protons 200.000000 k
1.558394 protons 210.000000 k
1.632603 protons 220.000000 k
1.706813 protons 230.000000 k
1.781022 protons 240.000000 k
1.855231 protons 250.000000 k
1.929440 protons 260.000000 k
2.003649 protons 270.000000 k <———-Two protons (helium) is k=270
2.077859 protons 280.000000 k
2.152068 protons 290.000000 k
2.226277 protons 300.000000 k
2.300486 protons 310.000000 k
2.374696 protons 320.000000 k
2.448905 protons 330.000000 k
2.523114 protons 340.000000 k
2.597323 protons 350.000000 k
2.671533 protons 360.000000 k
2.745742 protons 370.000000 k
2.819951 protons 380.000000 k
2.894160 protons 390.000000 k
2.968369 protons 400.000000 k
3.042579 protons 410.000000 k <—————-Three protons (Lithium) is k=400-410
3.116788 protons 420.000000 k
3.190997 protons 430.000000 k
3.265206 protons 440.000000 k
3.339416 protons 450.000000 k
3.413625 protons 460.000000 k
3.487834 protons 470.000000 k
3.562043 protons 480.000000 k
3.636253 protons 490.000000 k
3.710462 protons 500.000000 k
3.784671 protons 510.000000 k
3.858880 protons 520.000000 k
3.933089 protons 530.000000 k
4.007299 protons 540.000000 k <———— Four protons (Beryllium) is k=540
4.081508 protons 550.000000 k
4.155717 protons 560.000000 k
of 42 73
4.229927 protons 570.000000 k
4.304136 protons 580.000000 k
4.378345 protons 590.000000 k
4.452554 protons 600.000000 k
4.526763 protons 610.000000 k
4.600973 protons 620.000000 k
4.675182 protons 630.000000 k
4.749392 protons 640.000000 k
4.823600 protons 650.000000 k
4.897810 protons 660.000000 k
4.972019 protons 670.000000 k
5.046228 protons 680.000000 k. <———— Five protons (Boron) is k=680
5.120437 protons 690.000000 k
5.194647 protons 700.000000 k
5.268856 protons 710.000000 k
5.343065 protons 720.000000 k
5.417274 protons 730.000000 k
5.491484 protons 740.000000 k
5.565692 protons 750.000000 k
5.639902 protons 760.000000 k
5.714111 protons 770.000000 k
5.788321 protons 780.000000 k
5.862529 protons 790.000000 k
5.936739 protons 800.000000 k
6.010948 protons 810.000000 k <————— Six protons (carbon) is k=810
6.085157 protons 820.000000 k
6.159367 protons 830.000000 k
6.233576 protons 840.000000 k
6.307785 protons 850.000000 k
6.381995 protons 860.000000 k
6.456204 protons 870.000000 k
6.530413 protons 880.000000 k
6.604622 protons 890.000000 k
6.678832 protons 900.000000 k
6.753041 protons 910.000000 k
6.827250 protons 920.000000 k
6.901459 protons 930.000000 k
6.975668 protons 940.000000 k
7.049878 protons 950.000000 k <———— Seven protons (Nitrogen) is k=950
7.124087 protons 960.000000 k
7.198296 protons 970.000000 k
7.272505 protons 980.000000 k
7.346714 protons 990.000000 k
7.420924 protons 1000.000000 k
7.495133 protons 1010.000000 k
7.569342 protons 1020.000000 k
7.643551 protons 1030.000000 k
7.717761 protons 1040.000000 k
7.791970 protons 1050.000000 k
7.866179 protons 1060.000000 k
7.940388 protons 1070.000000 k
8.014598 protons 1080.000000 k. <———- Eight protons (Oxygen) is k=1080
8.088807 protons 1090.000000 k
8.163016 protons 1100.000000 k
of 43 73
Here are the orbital velocities for the planets:
Mercury 47,890 m/s
Venus 35,030 m/s
Earth 29,790 m/s
Mars 24,130 m/s
Jupiter 13,060 m/s
Saturn 9,640 m/s
Uranus 6,810 m/s
Neptune 5,430 m/s
Input a value for k:
140
Input a planetary orbital velocity: <—- k=140 (hydrogen) for Earth
29790
integer = 14.587176
Would you like to do another? 0=no, 1=yes
1
Input a value for k:
140
Input a planetary orbital velocity: <——k=140 (hydrogen) for Venus
35030
integer = 15.818164
Would you like to do another? 0=no, 1=yes
1
Input a value for k:
140
Input a planetary orbital velocity: <——-k=140 (hydrogen) for Mars
24130
integer = 13.128486
Would you like to do another? 0=no, 1=yes
0
Thank you.
Program ended with exit code: 0
Venus:integer=16
Mars: integer=13
And we can run it for :
x= 5.373682E-31
y= 2.630080E-12
(xy)= 1.413321E-42
q= 9.183727E-19
What is your value for 1/k? Our theoretical 1/k is 773.5:
11.936
q/charge= 0.088576 protons
What value do you want to start at for 1/k?: 0
By what value do you want to increment? 1
How many values would you like to calculate for q/proton (no more than 100?):
20
0.007421 protons 1.000000 k
0.014842 protons 2.000000 k
0.022263 protons 3.000000 k
0.029684 protons 4.000000 k
0.037105 protons 5.000000 k
0.044526 protons 6.000000 k
0.051946 protons 7.000000 k
0.059367 protons 8.000000 k
k
n
of 44 73
0.066788 protons 9.000000 k
0.074209 protons 10.000000 k
0.081630 protons 11.000000 k
0.089051 protons 12.000000 k <——-Value for 1/k for a neutron star
0.096472 protons 13.000000 k
0.103893 protons 14.000000 k
0.111314 protons 15.000000 k
0.118735 protons 16.000000 k
0.126156 protons 17.000000 k
0.133577 protons 18.000000 k
0.140998 protons 19.000000 k
0.148418 protons 20.000000 k
Here are the orbital velocities for the planets:
Mercury 47,890 m/s
Venus 35,030 m/s
Earth 29,790 m/s
Mars 24,130 m/s
Jupiter 13,060 m/s
Saturn 9,640 m/s
Uranus 6,810 m/s
Neptune 5,430 m/s
Input a value for k:
11.936
Input a planetary orbital velocity:
35030
integer = 54.173969 <———1/k produces integer 54 for for Venus
Would you like to do another? 0=no, 1=yes
1
Input a value for k:
11.936
Input a planetary orbital velocity:
29790
integer = 49.958092 <———1/k produces integer 50 for Earth
Would you like to do another? 0=no, 1=yes
1
Input a value for k:
11.936
Input a planetary orbital velocity:
24130
integer = 44.962376 <—————1/k produces integer 45 for Mars
Would you like to do another? 0=no, 1=yes
1
Input a value for k:
11.936
Input a planetary orbital velocity:
13060
integer = 33.078224 <—————1/k produces integer 33 for Jupiter
Would you like to do another? 0=no, 1=yes
1
Input a value for k:
11.936
Input a planetary orbital velocity:
9640
integer = 28.419022
Would you like to do another? 0=no, 1=yes
1
Input a value for k:
11.936
of 45 73
Input a planetary orbital velocity:
6810
integer = 23.886040
Would you like to do another? 0=no, 1=yes
1
Input a value for k:
11.936
Input a planetary orbital velocity:
5430
integer = 21.329000
Would you like to do another? 0=no, 1=yes
0
Thank you.
Program ended with exit code: 0
of 46 73
10.0 Orbital Velocity We can find our six-fold symmetry is characteristic of the solar system
as well. The Earth rotates through 15 degrees in one hour:
The distance then that the earth equatorial surface rotates through is where r is the earth
radius and theta is in radians.
Now we look at how many degrees through which the earth rotates in 1 minute:
For seconds…
Now let’s look at the same for the distance the earth moves around the Sun in an hour, a minute,
and a second as well…
And finally…
360
24
= 15
s = r θ
s = (6,378.14)(0.2618ra d ) = 1669.8k m /hr
24(60) = 1440min
360
1440
= 0.25
= 0.0043633ra d
s = (6,378.14)(0.00436) = 27.83k m /min
24(60)(60) = 86,400s
360
86,400
= 0.004167
= 0.00007272ra d
s = (6,378,14)(0.00007272) = 0.464k m /s
(365.25)(24) = 8766hr /yr
360
8766
= 0.041
= 0.00071678ra d
(149,598,000)(0.000716768) = 107,227k m /hr
(365.25)(24)(60) = 525960
360
525960
= = 0.000684463
= 0.000011946ra d
s = (149,598,000)(0.000011946) = 1,787.1k m /min
(365.25)(24)(60)(60) = 31557600
of 47 73
We have the following table:
As we can see I am in good
agreement with Martin
Zombek, Handbook of Space
Astronomy and Astrophysics
which provides data. Notice
27.83 km/min in earth
rotation is approximately the
29.786 km/sec in earth orbit.
That is a valuable clue. Now let
us consider
Earth: 1 AU=149,598,000km (average earth-sun separation).
The earth rotates through about one degree a day.
Earth Orbit:
Earth Rotation: r=6,378.14km
Moon: sidereal month =27.83 days, r=405,400 km
360
31557600
= 0.000011408
= 0.000000199ra d
(149,598,000)(0.000000199) = 29.786k m /sec
360
365.25
= 0.9856
deg
d ay
1
deg
d ay
360
= 2π r a dia n s = 6.283
ra d
year
0.9856
= 0.017202424
ra d
d ay
(149,598,000)(0.017202424) = 2,573,448.201
k m
d ay
360
1d ay
= 6.283
ra d
d ay
s = r θ = (6,378.14)(6.283) = 40,075.0
k m
d ay
(27.83)(24) = 667.92
h ours
m onth
360
667.92
= 0.529
= 0.0094
ra d
hr
of 48 73
The points to be made in this exploration
1. So the earth goes through 1 degree a day and the moon 1 kilometer per second.
2. Earth rotates through 27.83 km/min at its equatorial surface and orbits through 29.786km/s
around the sun. These two are close to the same.
3. The synodic month is 29.53 days approximately equals the 29.786 km/s the Earth moves
around the sun. The sidereal month is 27.83 days is the 27.83 km/min through which the
Earth rotates at its surface.
With that information we have this mystery of sexagesimal in the earth-moon-sun orbital
parameters, solved. We see we can make the following equation in table form:
Consider minute times day:
Thus,..
The circle is divided into 360 units, each unit (each degree) is the distance the earth moves
around the Sun in a day, where a day is one turn of the earth on its its axis, and as such there are
360 such turns in the time it takes the earth to go around the sun approximately (365.25 days).
We have:
1 astronomical unit (AU) is the distance of the earth from the sun on the average, and is always
close to that because its orbit is approximately circular. We have
This is approximately the diameter of the Earth orbit. We define our variables:
Earth orbits:
(405,400k m)(0.0094r a d /hr) = 3,810.76k m /hr
(3,810.75k m /hr)(hr /60min) = 63.5k m /min = 1.0585k m /s
orbit rotat ion orbit m oon
29.786k m minute 1d ay k ilom eter
secon d 27.83k m degr ee secon d
=
mi n d a y
deg
k m
s
2
(mi n)(d a y) = 60(24 60 60) = 864,000sec
2
mi n d a y
deg
k m
s
2
=
86,400s
2
deg
k m
s
2
= 86,400
k m
deg
86,400
k m
deg
360
= 311,040,000k m
311,040,000k m
149,598,000k m /AU
= 2.079AU
v
e
= 29.786
k m
s
of 49 73
Earth rotates:
Earth orbits:
Moon orbits:
Earth completes a 360 degree orbit yields:
Where on the right it is in radians and is the radius of the Earth’s orbit. We have
This is (0.00618)360=2.225
0.00618 is
Where is the inverse of the golden ratio. .
We have:
Equation 10.1
Our base ten counting is defined
is defined
, such that
which is given by
Thus since the diameter of the Earth orbit is
ω
e
=
27.83k m
mi n
=
27.83k m
mi n
mi n
60sec
= 0.4638
k m
sec
θ
e
=
1d ay
deg
=
(24)(60)(60)
deg
= 14,400
sec
deg
v
m
=
1k m
sec
v
e
θ
e
v
m
ω
e
360
1AU
= 2π
v
e
θ
e
v
m
ω
e
r
e
r
e
= 1AU
(29.786)(14,400)(1k m /s)
(0.4638)(149,598,000)
360 = 2.225AU
ϕ
100
ϕ
ϕ = 0.618 =
1
Φ
ϕ
100
360
= 2AU
10
0
= 1,10
1
= 1,10
2
= 100,...
ϕ
5 + 1
2
= Φ =
a
b
a
b
=
b
c
a = b + c
ϕ =
b
a
=
1
Φ
a
2
b
2
a
b
1 = 0
of 50 73
Then its radius is
Since we measure time with the Earth orbital period and that period is given by Kepler as
Then
Equation 10.2
Is approximately one year. In this section we set out two show the historical development of the
second by dividing up the motions of the Earth, Moon, and the apparent motion of the Sun into
units of 24, and 60 result in the solar system’s size as based around the Earth orbit giving us
Since we have established a connection between the microcosmos and the macrocosmos we
would do well to introduce the units of AU (astronomical unit), year, solar masses. Thus we want
to know the universal gravitational constant in these units:
For a year we have
(365.25)(24)(60)(60)=31557600 seconds
ϕ
100
360
= 2AU
1
2
ϕ
100
360
= 1AU
T
2
= a
3
T =
3
2
10
ϕ
3
2
10
3
360
ϕ
100
360
= 2AU
G = 6.67408E 11
m
3
kg s
2
G = 6.67408E 11
m
3
kg s
2
AU
3
3.3479E 33m
3
1.98847E 30kg
M
9.9477E14s
2
year
2
G = 39.433
AU
3
M
year
2
G 40
AU
3
M
year
2
GM
= 40
AU
3
year
2
GM
4π
2
= 0.99885 1
of 51 73
And for an AU
1 AU=1.496E11m
We can immediately put this to work. In order for the earth to stay in orbit its centripetal force
must equal the gravitational force. Its orbital velocity must be given by:
Since in our theory we present R as:
Then
Equation 10.3
Which evaluates:
Converting this to meters per second:
Which should be about right. The orbital velocity is given in the data tables as about 30,000m/s
is an average over a varying velocity due to the Earth’s slightly elliptical orbit.
Since we have
For the earth, we show now it is true for the moon as well, and indeed it would hold for any
system circular, or approximately circular. For the Sun and its planets
If you use astronomical units and Earth years. In general we use
G
Mm
R
2
=
mv
2
r
v =
GM
R
1
2
ϕ
100
360
= 1AU
v =
5
3
GM
ϕ
v =
5
3
(40)(1)
0.618
= 6
AU
year
6
AU
year
year
3.156E 7
1.496E11m
AU
= 28,441
m
s
1
2
ϕ
100
360
= 1AU
T
2
= a
3
of 52 73
Which has the constant of proportionality
If m is small compared with M, you can write
Since we want to work with Earth and the Moon m is not so small compared to M. So,…
=
=
And these do round neatly to one-exponent like this. The sidereal lunar month is
(27.83)(24)(60)(60)=2,404,513 seconds. Thus,…
The tables give
Which is an average for the lunar orbit in its slightly elliptical orbit.
We need to find G in terms of Lunar Units (LU) as opposed to Astronomical Units (AU), and in
terms of the lunar month as one instead of the earth year. We see G has the same value we had
for solar-earth units:
=
T
2
= G
M + m
4π
2
a
3
1
k
= G
M + m
4π
2
1
k
= G
M
4π
2
1
k
= (6.674E 11)
(
5.9722E 24kg + 7.347731E 22kg
4π
2
)
(6.674E 11)
(
6E 24kg
4π
2
)
4E14
4π
2
=
1E14
π
2
= 1E13
a
3
= (1E13)(2,404,512)
2
= 5.78E 25
a = 3.8668E8m
a = 3.833E8m
G = 6.674E 11
m
3
kg s
2
LU
3
(3.8668E8m)
3
5.9722E 24kg
M
(2,404,512s)
2
L M
2
40.896
LU
3
M
L M
2
of 53 73
We only need to convert to m, kg, s by using their relationships with LU, LM, and . That is,
for the orbital velocity is always six:
Where is the orbital velocity of the moon, and is the orbital velocity of the earth. The
difference comes when converting the system from lunar units in the case of the first to kg/m/s
and from astronomical units in the case of the second to kg/m/s. For example the first is:
Which is correct, the tables give that the lunar orbital velocity is 1000 m/s.
To find logos, is to find Nature not just as number, but as dimensionless whole
number, because fractions have inherent in them irrational numbers, which are
unending decimal expressions that at some point must be rounded to so many
figures to put them to use. Logos then is the language of Nature that transcends
conundrum because it would be utilized as relationship between point, plane, and
line as opposed to units. We have found that for the orbital velocity:
Equation 10.4
Where is the earth orbital radius. This results in the orbital velocity for a orbiting body is
Equation 10.5
Which is logos because it is number, which is 6. The orbital velocity of a body is always 6
because:
Where is the orbital velocity of the moon, and is the orbital velocity of the earth, That is G
is always 40, and M is always 1 providing the orbit is circular. Let us show this for Venus. Its
M
v
m
=
5
3
(40)(1)
ϕ
= 6
v
e
=
5
3
(40)(1)
ϕ
= 6
v
m
v
e
v
m
= 6
3.8668E8m
2,404,512s
= 964.886m /s
R
e
=
1
2
ϕ
100
360
= 1AU
R
e
v =
5
3
GM
ϕ
v
m
=
5
3
(40)(1)
ϕ
= 6
v
e
=
5
3
(40)(1)
ϕ
= 6
v
m
v
e
of 54 73
orbital distance VU (Venus units) is 1.082E11meters. It orbital period is 1.94E7s is the Venus
year (VY).
=
Thus we have
We can then express all orbital velocities as 6, but to find there values in a formal system of
units, we need to convert from these natural units to something like kg/m/s. Thus logos
translated into a language we understand can best be done in a square array, or as a matrix
transformation. We have
You will find this gives , ,
All of which are correct within the variations of these velocities in their deviations from a
perfectly circular orbit. Logos is:
Equations 10.6
G = 6.674E 11
m
3
kg s
2
LU
3
(1.082E11m)
3
1.989E 30kg
M
(1.94E 7s)
2
V Y
2
39.44
V U
3
M
V Y
2
40
v
v
=
5
3
(40)(1)
ϕ
= 6
(
6 6 6
)
3.8668E8m
2,404,512s
1.496E11m
31,557,600s
1.082E11m
19,400,000s
=
v
m
v
e
v
v
v
m
= 964.886m /s
v
e
= 28,443m /s
v
v
= 33,463.9m /s
(
5
3
GM
ϕ
5
3
GM
ϕ
5
3
GM
ϕ
)
R
m
T
m
R
e
T
e
R
v
T
v
=
v
m
v
e
v
v
=
6
6
6
R
m
=
1
2
ϕ
100
360
= 1LU
R
e
=
1
2
ϕ
100
360
= 1AU
R
v
=
1
2
ϕ
100
360
= 1V U
of 55 73
, such that
which is given by
To say that logos is:
Is to say that for the solar system Kepler’s Law of Planetary Motion holds:
That in general
Because as such for Earth we have
For the Moon we have
For Venus we have
v =
5
3
GM
ϕ
5 + 1
2
= Φ =
a
b
a
b
=
b
c
a = b + c
ϕ =
b
a
=
1
Φ
a
2
b
2
a
b
1 = 0
(
6 6 6
)
3.8668E8m
2,404,512s
1.496E11m
31,557,600s
1.082E11m
19,400,000s
=
v
m
v
e
v
v
T
2
= a
3
T
2
= G
M + m
4π
2
a
3
G = 6.67408E 11
m
3
kg s
2
AU
3
3.3479E 33m
3
1.98847E 30kg
M
9.9477E14s
2
year
2
G 40
AU
3
M
year
2
G = 6.674E 11
m
3
kg s
2
LU
3
(3.8668E8m)
3
5.9722E 24kg
M
(2,404,512s)
2
L M
2
40.896
LU
3
M
L M
2
of 56 73
Making
, ,
This is derived from
Which is to say
Is logos because
such that
which is given by
G = 6.674E 11
m
3
kg s
2
V U
3
(1.082E11m)
3
1.989E 30kg
M
(1.94E 7s)
2
V Y
2
39.44
V U
3
M
V Y
2
40
v
e
=
5
3
(40)(1)
ϕ
= 6
v
m
=
5
3
(40)(1)
ϕ
= 6
v
v
=
5
3
(40)(1)
ϕ
= 6
G
Mm
R
2
=
mv
2
R
v =
GM
R
1
2
ϕ
100
360
= 1AU
R
m
=
1
2
ϕ
100
360
= 1LU
R
e
=
1
2
ϕ
100
360
= 1AU
R
v
=
1
2
ϕ
100
360
= 1V U
v =
5
3
GM
ϕ
5 + 1
2
= Φ =
a
b
a
b
=
b
c
a = b + c
ϕ =
b
a
=
1
Φ
a
2
b
2
a
b
1 = 0
of 57 73
Which is the relationship between point, plane, and line.
From everything we have said G, the gravitational constant is about 40
We can do this for any planet and get G is approximately 40. We found the orbital velocity of any
planets is 6. This is true because as we have shown, the orbital distance of any planet is
This gives since
That orbital velocities are for the moon, earth, and venus
But what does this mean? It means since
And, v=6, that where the orbital velocities of the planets are 6, their distances from the sun are
all one.
This gives:
But where six is
G = 6.674E 11
m
3
kg s
2
AU
3
(Ear th Dista nceMeters)
3
Sol arMa ssKilogra m s
M
(Ear thOrbit a l Per iod Secon d s)
2
year
2
1
2
ϕ
100
360
= 1AU
v =
GM
R
=
5
3
GM
ϕ
(
6 6 6
)
3.8668E8m
2,404,512s
1.496E11m
31,557,600s
1.082E11m
19,400,000s
=
v
m
v
e
v
v
R =
GM
v
2
R =
40
36
1
(
1 1 1
)
3.8668E8m
1.496E11m
1.082E11m
=
R
m
R
e
R
v
of 58 73
Since we have
And since we have said
Which we can write
Equation 10.7
Where r and T are orbital radii and orbital periods subscripted with their designations, then we
see Earth is the eigenvalue because
Equation 10.8
Which means
Or,…
Equation 10.9
That is since Eigenvalues are characteristic roots, that is the value such that for the matrix A:
(
6 6 6
)
3.8668E8m
2,404,512s
1.496E11m
31,557,600s
1.082E11m
19,400,000s
=
v
m
v
e
v
v
k v
e
= 6
(
6 6 6
)
3.8668E8m
2,404,512s
1.496E11m
31,557,600s
1.082E11m
19,400,000s
=
v
m
v
e
v
v
(
6 6 6
)
r
m
/T
m
r
e
/T
e
r
v
/T
v
=
v
m
v
e
v
v
(
6 k v
e
6
)
r
m
/T
m
r
e
/T
e
r
v
/T
v
=
v
m
v
e
v
v
k v
e
r
e
T
e
= v
e
k
r
2
e
T
2
e
= v
e
λ
A
x = λ
x
of 59 73
!
Since!
!
Implies!
!
Where!
!
Is the identity matrix. Then we see these are the the eigenvalues and , because!
!
Which is!
!
!
Which are the polynomials!
and !
Which means the eigenvectors are!
and !
Because!
and,…!
!
A =
(
4 1
6 3
)
A
u = λ
u
A λI =
0
I =
(
1 0
0 1
)
λ = 6
λ = 1
(
4 1
6 3
)
λ
(
1 0
0 1
)
=
(
4 λ 1
1 3 λ
)
=
0
λ
2
7λ + 6 = 0
(λ 1)(λ 6) = 0
y 2x = 0
y + 3x = 0
(
x
y
)
=
(
1
3
)
(
x
y
)
=
(
1
2
)
(
4 1
6 3
)(
1
3
)
= 1
(
1
3
)
(
4 1
6 3
)(
1
2
)
= 6
(
1
2
)
of 60 73
The matrix!
!
Is a linear transformation for which the eigenvectors!
and !
Point in a direction in which the eigenvalue is stretched, and the eigenvalues!
and !
Are the factors by which it is stretched.!
A =
(
4 1
6 3
)
(
x
y
)
=
(
1
3
)
(
x
y
)
=
(
1
2
)
(
x
y
)
=
(
1
3
)
(
x
y
)
=
(
1
2
)
of 61 73
!
Thus our transformation is!
!
Which is!
!
!
!
!
Thus everywhere in the planes below these
surfaces the vectors!
!
!
Point in the direction of the steepness of the
slopes of these planes respectively, and their
steepness are!
!
!
Respectively. We have done all of this so we
can visualize what is meant by the earth is the
eigenvalues for the matrix that is the matrix for
the orbits of the planets. In as much as we
have said:!
Which is to say
T(
u ) =
(
4 1
6 3
)(
x
y
)
f (x, y) = 4x + y
g(x, y) = 6x + 3y
f (x, y) = 4
i + 1
j
g(x, y) = 6
i + 3
j
4
i + 1
j
6
i + 3
j
4
2
+ 1
2
= 17 = 4.123
6
2
+ 3
2
= 45 = 6.71
6
r
m
/T
m
r
e
/T
e
r
v
/T
v
=
v
m
v
e
v
v
6
r
m
/T
m
r
e
/T
e
r
v
/T
v
=
964.886m /s
28,443m /s
33,463.8m /s
of 62 73
Where we have taken the moon, Earth, and Venus as examples, but which works for any orbiting
body, and 6 is in!
!
And is !
!
We are essentially saying!
!
And we want to find A. Since has no units, and on the right we must have!
!
Because these are the respective orbital velocities of the moon, Earth, and Venus, then!
!
That is!
!
And we have our eigenvectors are!
and. "
λ
λ
x = A
x
x
r
m
/T
m
r
e
/T
e
r
v
/T
v
=
v
m
v
e
v
v
λ
r
m
/T
m
r
e
/T
e
r
v
/T
v
= A
6
6
6
λ
λ
r
m
/T
m
r
e
/T
e
r
v
/T
v
=
964.886m /s
28,443m /s
33,463.8m /s
A =
160.814m /s
4,740.5m /s
5,577.3m /s
λ
r
m
/T
m
r
e
/T
e
r
v
/T
v
=
160.814m /s
4,740.5m /s
5,577.3m /s
6
6
6
(
x
y
z
)
=
r
m
/T
m
r
e
/T
e
r
v
/T
v
(
x
y
z
)
=
6
6
6
of 63 73
We have!
!
!
!
And for the condition of eigenvectors to be satisfied by eigenvalues we have to have!
!
!
!
Which is to say!
!
And that is what we want to show. We have said that!
And, since !
And we showed that!
λ
r
m
/T
m
r
e
/T
e
r
v
/T
v
= A
6
6
6
λ = 6
A =
160.814m /s
4,740.5m /s
5,577.3m /s
λ
6
6
6
= A
6
6
6
λ
r
m
/T
m
r
e
/T
e
r
v
/T
v
= A
r
m
/T
m
r
e
/T
e
r
v
/T
v
A =
160.814m /s
4,740.5m /s
5,577.3m /s
r
m
/T
m
r
e
/T
e
r
v
/T
v
=
6
6
6
1
2
ϕ
100
360
= 1AU
v =
GM
r
r
e
=
1
2
ϕ
100
360
= 1AU
of 64 73
!
We have shown that!
!
!
Which holds for all orbiting bodies if we use their natural units, like for Venus!
!
Where VU is Venus units as opposed to Earth Units (Astronomical Units). Thus for the Earth!
!
Because !
!
Meaning the units of phi are !
Since we have that!
!
Where means G in Natural System units means if your are working with earth you are
using astronomical units and earth years, if with Venus Venus units and so on. But so!
!
That the two eigenvectors!
v =
5
3
GM
ϕ
G = 6.67408E 11
m
3
kg s
2
AU
3
3.3479E33m
3
1.98847E30kg
M
9.9477E14s
2
year
2
G 40
AU
3
M
year
2
G = 6.674E 11
m
3
kg s
2
VU
3
(1.082E11m)
3
1.989E30kg
M
(1.94E 7s)
2
V Y
2
v
e
=
5
3
40(1)
ϕ
M
= 1
v
e
=
AU
3
M
year
2
ϕ
ϕ =
M
AU
ϕ 5 /3
v
e
G
NS
M
G
NS
M
= 1
v
e
= G
NS
= 40 6
of 65 73
!
Are equal and hence the condition for our eigenvectors!
!
!
Is satisfied because it can be written!
Equation 10.10. !
Where A is!
Equation 10.11. !
Which is what we want because we want!
Equation 10.12 !
Where:!
Which is
or Is Natural System Units!
r
m
/T
m
r
e
/T
e
r
v
/T
v
=
6
6
6
λ
6
6
6
= A
6
6
6
λ
r
m
/T
m
r
e
/T
e
r
v
/T
v
= A
r
m
/T
m
r
e
/T
e
r
v
/T
v
λ
r
m
/T
m
r
e
/T
e
r
v
/T
v
= A
6
6
6
A =
160.814m /s
4,740.5m /s
5,577.3m /s
λ = k v
e
k =
4
3
m
p
8π
3
G
c
3
h
(1 + α) N
A
𝔼
1
k
= 773.5m /s
6
(
r
e
T
e
)
= G
NS
= 6
r
e
T
e
= 1
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11.0 Conclusion
Indeed we have shown that we can predict the radius of a proton and its mass in terms
of the properties of space:!
Which gives
And the interesting thing is they do not yet have an equation for the radius of a proton, yet we
have it here and it doesn’t just use Planck’s constant, h, of the indeterministic microcosmos, but
uses the gravitational constant, G, of the deterministic macrocosmos.
We have further shown our theory of inertia is based on six-fold symmetry is centered around
hydrocarbons, the skeletons of life chemistry
We find 1 second gives
We find six seconds gives 1 proton is hydrogen:
We further find this same sixfold symmetry describes not just proton systems (atoms) but our
solar system
My feeling is if we want to go further to explain why six-fold symmetry we have to go into the
mathematics of symmetry breaking and perturbation theory. A particle has an equal problem of
falling either left or right out of an unstable equilibrium into wells on either to the left of it or
right. In the mathematics we say that even though there is an equal probability of going to the
left as opposed to the right or vice versa, one is magically chosen over the other, because we
don’t say a force exists that choses a direction, but use the word perturbation. But is a
perturbation a small force that has a preference as to which direction something will go?
Whether it it is, or not, is not clear because by quantum mechanics the particles does not have a
position, just a probability of existing in a given region at a given time. But does this mean if a
choice is made of falling in one direction or the other that there exists something physical going
r
p
=
1
m
p
hc
2π
3
G
R
H
N
A
𝔼
r
p
= 8.26935E 16m 0.827f m
1
α
2
m
p
h 4π r
2
p
Gc
= 6pr oton secon ds = carbon(C )
1
α
2
m
p
h 4π r
2
p
Gc
= 1pr oton 6secon d s = hydr ogen(H )
(
6 6 6
)
r
m
/T
m
r
e
/T
e
r
v
/T
v
=
v
m
v
e
v
v
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on that we can explain that explains why the quantum mechanics is the way it is? Currently
quantum mechanics cannot describe anything deterministic, but only works in probabilities.
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Appendix 1
We suggested the second was a natural unit, and that, if it was, should be in the orbital
mechanics of the earth because the second comes from the calendar, which is based on the
orbital period of the year (1 year, 365.25 days) and the orbital period of the moon, and the
rotation of the Earth. We found that it was as the following:
Let’s show that…
To find the translational kinetic energy of the moon:
Distance from earth: 3.85E8m
Orbital period:
T=27.32 days=2.36E6seconds
v=1.025E3m/s~1000m/s
Mass: 7.34767E22kg
Use
E=3.67E28 Joules
To find the translational kinetic energy of the earth:
Distance from Sun: 1AU=1.496E11m
Orbital period: 1 year=3.1558E7 seconds
v=2.9785E4m/s, Earth mass: 5.9722E24kg
E=2.649E33 Joules
Earth day=(24)(60)(60)=86,400 seconds.
K E
moon
K E
earth
(Ear th Da y) 1secon d
K . E . Moon = 3.67E 28J
K . E . Ear th = 2.649E 33j
2π (3.85E 8m) = 2.419E 9m
E =
1
2
mv
2
2π (1.496E11m) = 9.399E11m
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Appendix 2: Sexagesimal And The Cosmic Calendar
My book Abstract Cosmology could have easily been called The Book of Six, it was
Buckminster Fuller who said “Nature employs 60 degree coordination”. Sixty degrees are the
degrees of an equilateral triangle. The triangle is the structure that encloses an area with the
least amount of sides. Buckminster Fuller said, systems of triangles are the the only inherently
stable patterns. The regular hexagon, a six-sides polygon tessellates as equilateral, 60 degree,
inherently stable equilateral triangles. It was the scientist Shubnikov who said among the living
organisms the pattern with which we most frequently meet is five-fold symmetry. It is well
known that the physical, like snowflakes, are six-fold symmetry. Thus we should not be
surprised that our Abstract Cosmology is founded on six-fold symmetry. Two and three are the
smallest prime numbers and their product is six. Two times six is twelve, the number most
evenly divisible by whole numbers for its size (it is a so-called abundant number: divisible
evenly by 1,2,3,4,6, their sum is 16 which is greater than twelve itself and, three times six is
eighteen, the cyclical Nature of the periodic table (18 groups). !
At the dawn of civilization, the Sumerians who settled down from wandering, gathering, and
hunting, to invent agriculture and and build ceramic homes, developed the first mathematics,
and it was this sexagesimal (base 60) that passed on to the Babylonians, then ended up with
the Ancient Greeks, who divided not just the hour into 60 minutes of time and the minute into
60 seconds of time, but who divided the sky into hours, minutes, and seconds of arc which
was measured in time counted by the rotation of the Earth, and its orbital period around the
Sun, and the orbital period of the Moon around the Earth.!
We are suggesting nature is founded on six-fold symmetry, six which is constructed by
multiplying together the first two prime numbers, 2 and 3. Two factorial is two, three factorial is
6. Two times six is twelve, the number of months in a year, approximated by our moon’s
approximately 12 orbits around the earth in the time it takes the earth to go around the sun
once. There are four weeks in a lunar month, and!
!
Is the number of seconds in the 24 hour Earth day. The duration of one second comes from
dividing up time and the sky like this in base 60, that came from the Sumerians, Babylonians,
and Ancient Greeks and it is believed they did this because 60 is evenly divisible by!
1,2,3,4,5,6,…12,15,20,30,60,…!
The moon orbits the Earth in approximately 30 rotations of the Earth, hence the 30 day month.
January has 31 days, February 29, March 31, April 30 May 31, June 30, July 31, August 31,
September 30, October 31, November 30, December 31. This averages out to!
!
We divide a circle into 360 units called degrees, which is six squared times ten. As such the
equilateral triangle has each angle equal to 60 degrees. There are approximately 360 earth
rotations in the time it orbits the sun once, Hence in one day the Earth moves through
approximately one degree in one day in its 365 day journey around the Sun. The sidereal
month, the time it takes the moon to return to the same position against the background of the
stars is 27 days 7 hours 43 minutes. We see the power of sexagesimal (base 60) in computing
time with the month divided into days, hours, and seconds where there are 60 minutes in an
1 2 3 4 60
2
= 86,400
31 + 29 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 30 + 31
12
=
367
12
= 30.58333
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hour and 60 seconds in a minute because we can convert this easily into seconds with such a
system as here, the duration of this sidereal month in seconds:!
!
The length of the synodic month, the completion of the phases of the moon, or the time it takes
the moon to return to the same position with respect to the Sun, is 29 days 12 hours 44
minutes 3 seconds. It is a little longer than the sidereal month because the earth has moved
with respect to the sun by the time the moon has come back around to a full orbit. We have:!
!
We looked at the arithmetic mean of the days in the month over a year, Let us look at the
harmonic mean:!
=!
!
Gathering like terms in the denominator:!
=0.225806+0.034482759+0.133333=0.39362!
!
Which is the most frequent value for the days in a month. Now let’s look at the geometric mean
which tempers the various values with one another.!
=30.493!
But perhaps it is more telling to take the mean between the individual days of the month that
we use:!
!
!
0.032258+0.034482759+0.033333=0.10007!
!
!
(24 27 + 7) 60
2
+ 43 60
1
+ 0 60
0
= 2,358,000 + 2,580 + 0 = 2360580sec/month
(24 29 + 12) 60
2
+ 44 60
1
+ 3 60
0
= 2,548,800 + 2,640 + 3 = 2551443sec /month
12
1
31
+
1
29
+
1
31
+
1
30
+
1
31
+
1
30
+
1
31
+
1
31
+
1
30
+
1
31
+
1
30
+
1
31
12
0.032258 + 0.034482759 + 0.032258 + 0.033333 + 0.032258 + 0.033333 + 0.032258 + 0.032258 + 0.033333 + 0.032258 + 0.033333 + 0.032258
12
0.39362
= 30.486
12
31 29 31 30 31 30 31 31 30 31 30 31
31 + 29 + 30
3
=
90
3
= 30
3
1
31
+
1
29
+
1
30
3
0.10007
= 29.799 30
3
31 29 30 = 29.98888 30
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We see that the arithmetic mean gives us exactly a 30 day month, hence we always speak
loosely saying a month is 30 days. !
Indeed when Buckminster Fuller speaks of Nature employing 60 degree coordination he is
speaking of the equilateral triangle as the fundamental unit of one for area. That is the six-sided
regular hexagon can be divided into six equilateral triangles, giving it an area of six. Indeed he
takes the equilateral triangle as one because not only does it enclose an area with the fewest
sides, it has the smallest area for its perimeter; a regular hexagon with a perimeter the same
size encloses more area. I would like to say the Ancient Sumerians, Babylonians, and Greeks
made this connection, because in their sexagesimal (base 60) system of notation, one is a
straight line with a triangle on top. See figure below. Ancient Mesopotamian Cuneiform for
writing. It is not sexagesimal notation in the strict sense, as they have a unique symbol for a
tens column, but it was this sexagesimal structure that lead to the 60 minute hour and 60
second minute, as well as the angular division projected onto the sky in 60 minutes of arc in a
degree and 60 seconds of arc in a minute as a way of mathematically defining time dynamically
in terms of the motions of the Earth and moon.!
For equation our equation Earth day needs to be shorter. A long time ago it
was; the Earth loses energy to the moon. The days become longer by 0.0067
hours per million years. Our Equation
Is actually 1.2 seconds.
K E
moon
K E
earth
(Ear th Da y) 1secon d
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We have
24-20=0.0067t
t=597 million years
This was when the earth went through a dramatic change and there was a big explosion of life
(The Cambrian). The dinosaurs went extinct 65 million years ago giving small mammals a
chance to evolve paving the way for humans.
24-x=0.0067t
x=23.5645 hours
We say 20 hours + 3 hours is 0 hours + 3 hours since 20 hours is the zero of our cosmic
calendar:
What is the next term?
20+3+0.57735+0.4714=24hours
Which bring us to today.
It would seem we could have divided that day, not into 24 hours but 20 hours and get our 1.2
seconds as a duration for measuring time:
Both work because
24=2x2x6
20=>20+20+20=60
Both have an intimate structural relationships with sexagesimal.
24h ours
1.2
= 20h ours
3cos(0
) +
2
3
cos(30
) = din osaur ex t inct ion =
20hrs + 3hrs +
3
3
hrs +
2
3
=
(365.25d ays)(24hours)(60sec)(60sec)
(365.25d ays)(20hours)(60sec)(60sec)
= 1.2
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The Author